| Title:
|
Ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces (English) |
| Author:
|
Sato, Ryotaro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
77-88 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove ratio Tauberian theorems for relatively bounded functions and sequences in Banach spaces. (English) |
| Keyword:
|
ratio Tauberian theorem |
| Keyword:
|
$\gamma$-th order Cesàro integral |
| Keyword:
|
Laplace integral |
| Keyword:
|
$\gamma$-th order Cesàro sum |
| Keyword:
|
Abel sum |
| MSC:
|
40E05 |
| MSC:
|
47A35 |
| idZBL:
|
Zbl 1240.40025 |
| idMR:
|
MR2828369 |
| . |
| Date available:
|
2011-03-08T17:37:51Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141429 |
| . |
| Reference:
|
[1] Arendt W., Batty C.J.K., Hieber M., Neubrander F.: Vector-valued Laplace Transforms and Cauchy Problems.Monographs in Mathematics Vol. 96, Birkhäuser, Basel, 2001. MR 1886588 |
| Reference:
|
[2] Chen J.-C., Sato R.: Ratio limit theorems and Tauberian theorems for vector-valued functions and sequences.J. Math. Anal. Appl. 367 (2010), 108–115. Zbl 1194.40004, MR 2600382, 10.1016/j.jmaa.2009.12.047 |
| Reference:
|
[3] Chen J.-C., Sato R., Shaw S.-Y.: Growth orders of Cesàro and Abel means of functions in Banach spaces.Taiwanese J. Math. 14 (2010), 1201–1248. MR 2674604 |
| Reference:
|
[4] Emilion R.: Mean-bounded operators and mean ergodic theorems.J. Funct. Anal. 61 (1985), 1–14. Zbl 0562.47007, MR 0779737, 10.1016/0022-1236(85)90037-0 |
| Reference:
|
[5] Li Y.-C., Sato R., Shaw S.-Y.: Convergence theorems and Tauberian theorems for functions and sequences in Banach spaces and Banach lattices.Israel J. Math. 162 (2007), 109–149. Zbl 1142.40002, MR 2365856, 10.1007/s11856-007-0091-x |
| Reference:
|
[6] Li Y.-C., Sato R., Shaw S.-Y.: Ratio Tauberian theorems for positive functions and sequences in Banach lattices.Positivity 11 (2007), 433–447. Zbl 1127.40003, MR 2336207, 10.1007/s11117-007-2085-7 |
| Reference:
|
[7] Sato R.: On means of Banach-space-valued functions.Math. J. Okayama Univ.(to appear). |
| Reference:
|
[8] Widder D.V.: An Introduction to Transform Theory.Academic Press, New York and London, 1971. Zbl 0219.44001 |
| Reference:
|
[9] Zygmund A.: Trigonometric Series. Vol. I.Cambridge University Press, Cambridge, 1959. Zbl 0367.42001, MR 0107776 |
| . |
